Aristotle
(Aristoteles) quod demonstrare debebat ex ipsâ ratione quam singuli
termini inter se habeant: est enim proprium artis logicæ, ut
terminorum rationem cognoscat, dum res ignoret. Num de Caio
prædicetur animal nescit, scit de Caio prædicari animal, si animal de
homine et homo de Caio prædicetur."
This comment of Waitz appears to me founded in error. Aristotle had
no means of shewing the invalidity of the mode A E in the First
figure, except by an appeal to particular examples. The invalidity of
the invalid modes, and the validity of the valid modes, rest alike
upon this ultimate reference to examples of propositions known to be
true or false, by prior experience of the learner. The valid modes
are those which will stand this trial and verification; the invalid
modes are those which will not stand it. Not till such verification
has been made, is one warranted in generalizing the result, and
enunciating a formula applicable to unknown particulars (rationem
terminorum cognoscere, dum res ignoret). It was impossible for
Aristotle to do what Waitz requires of him. I take the opposite
ground, and regret that he did not set forth the fundamental test of
appeal to example and experience, in a more emphatic and
unmistakeable manner.
M. Barthélemy St. Hilaire (in the note to his translation, p. 14)
does not lend any additional clearness, when he talks of the
"_conclusion_" from the propositions A and E in the First figure.
Julius Pacius says (p. 134): "Si tamen _conclusio_ dici debet, quæ
non colligitur ex propositionibus," &c. Moreover, M. St. Hilaire (p.
19) slurs over the legitimate foundation, the appeal to experience,
much as Aristotle himself does: "Puis prenant des exemples où la
_conclusion est de toute évidence_, Aristote les applique
successivement à chacune de ces combinaisons; celles qui donnent la
_conclusion fournie d'ailleurs par le bon sens_, sont concluantes ou
syllogistiques, les autres sont asyllogistiques."]
We are now introduced to the Second figure, in which each of the two
premisses has the middle term as Predicate.[29] To give a legitimate
conclusion in this figure, one or other of the premisses must be
negative, and the major premiss must be universal; moreover no
affirmative conclusions can ever be obtained in it--none but negative
conclusions, universal or particular. In this Second figure too,
Aristotle recognizes four valid modes; setting aside the other
possible modes as invalid[30] (in the same way as he had done in the
First figure), because the third proposition or conjunction of the
major term with the minor, might in some cases be a true universal
affirmative, in other cases a true universal negative. As to the
third and fourth of the valid modes, he demonstrates them by assuming
the contradictory of the conclusion, together with the major premiss,
and then showing that these two premisses form a new syllogism, which
leads to a conclusion contradicting the minor premiss. This method,
called _Reductio ad Impossibile_, is here employed for the first
time; and employed without being ushered in or defined, as if it were
familiarly known.[31]
[Footnote 29: Analyt. Prior. I. v. p. 26, b. 34. As Aristotle
enunciates a proposition by putting the predicate before the subject,
he says that in this Second figure the middle term comes [Greek:
prô=ton tê=| the/sei]. In the Third figure, for the same reason, he
calls it [Greek: e)/schaton tê=| the/sei], vi. p. 28, a. 15.]
[Footnote 30: Analyt. Prior. I. v. p. 27, a. 18. In these invalid
modes, Aristotle says there is no _syllogism_; therefore we cannot
properly speak of a _conclusion_, but only of a third proposition,
conjoining the major with the minor.]
[Footnote 31: Ibid. p. 27, a. 15, 26, seq. It is said to involve
[Greek: u(po/thesis], p. 28, a. 7; to be [Greek: e)x u(pothe/seôs]
xxiii. p. 41, a. 25; to be [Greek: tou= e)x u(pothe/seôs], as opposed
to [Greek: deiktiko/s], xxiii. p. 40, b. 25.
M. B. St. Hilaire remarks justly, that Aristotle might be expected to
define or explain what it is, on first mentioning it (note, p. 22).]
Lastly, we have the Third figure, wherein the middle term is the
Subject in both premisses. Here one at least of the premisses must be
universal, either affirmative or negative. But no universal
conclusions can be obtained in this figure; all the conclusions are
particular. Aristotle recognizes six legitimate modes; in all of
which the conclusions are particular, four of them being affirmative,
two negative. The other possible modes he sets aside as in the two
preceding figures.[32]
[Footnote 32: Ibid. I. vi. p. 28, a. 10-p. 29, a. 18.]
But Aristotle assigns to the First figure a marked superiority as
compared with the Second and Third. It is the only one that yields
perfect syllogisms; those furnished by the other two are all
imperfect. The cardinal principle of syllogistic proof, as he
conceives it, is--That whatever can be affirmed or denied of a whole,
can be affirmed or denied of any part thereof.[33] The major
proposition affirms or denies something universally respecting a
certain whole; the minor proposition declares a certain part to be
included in that whole. To this principle the four modes of the First
figure manifestly and unmistakably conform, without any
transformation of their premisses. But in the other figures such
conformity does not obviously appear, and must be demonstrated by
reducing their syllogisms to the First figure; either ostensively by
exposition of a particular case, and conversion of the premisses, or
by _Reductio ad Impossibile_. Aristotle, accordingly, claims
authority for the Second and Third figures only so far as they can be
reduced to the First.[34] We must, however, observe that in this
process of reduction no new evidence is taken in; the matter of
evidence remains unchanged, and the form alone is altered, according
to laws of logical conversion which Aristotle has already laid down
and justified. Another ground of the superiority and perfection which
he claims for the First figure, is, that it is the only one in which
every variety of conclusion can be proved; and especially the only
one in which the Universal Affirmative can be proved--the great aim
of scientific research. Whereas, in the Second figure we can prove
only _negative_ conclusions, universal or particular; and in the
Third figure only _particular_ conclusions, affirmative or
negative.[35]
[Footnote 33: Ibid. I. xli. p. 49, b. 37: [Greek: o(/lôs ga\r o(\ mê/
e)stin ô(s o(/lon pro\s me/ros kai\ a)/llo pro\s tou=to ô(s me/ros
pro\s o(/lon, e)x ou)deno\s tô=n toiou/tôn dei/knusin o( deiknu/ôn,
ô(/ste ou)de\ gi/netai sullogismo/s.]
He had before said this about the relation of the three terms in the
Syllogism, I. iv. p. 25, b. 32: [Greek: o(/tan o(/roi trei=s ou(/tôs
e)/chôsi pro\s a)llê/lous ô(/ste to\n e)/schaton e)n o(/lô| ei)=nai
tô=| me/sô| kai\ to\n me/son e)n o(/lô| tô=| prô/tô| ê)\ ei)=nai ê)\
mê\ ei)=nai, a)na/gkê tô=n a)/krôn ei)=nai sullogismo\n te/leion]
(_Dictum de Omni et Nullo_).]
[Footnote 34: Analyt. Prior. I. vii. p. 29, a. 30-b. 25.]
[Footnote 35: Ibid. I. iv. p. 26, b. 30, p. 27, a. 1, p. 28, a. 9, p.
29, a. 15. An admissible syllogism in the Second or Third figure is
sometimes called [Greek: dunato\s] as opposed to [Greek: te/leios],
p. 41, b. 33. Compare Kampe, Die Erkenntniss-Theorie des Aristoteles,
p. 245, Leipzig, 1870.]
Such are the main principles of syllogistic inference and rules for
syllogistic reasoning, as laid down by Aristotle. During the mediæval
period, they were allowed to ramify into endless subtle
technicalities, and to absorb the attention of teachers and studious
men, long after the time when other useful branches of science and
literature were pressing for attention. Through such prolonged
monopoly--which Aristotle, among the most encyclopedical of all
writers, never thought of claiming for them--they have become so
discredited, that it is difficult to call back attention to them as
they stood in the Aristotelian age. We have to remind the reader,
again, that though language was then used with great ability for
rhetorical and dialectical purposes, there existed as yet hardly any
systematic or scientific study of it in either of these branches. The
scheme and the terminology of any such science were alike unknown,
and Aristotle was obliged to construct it himself from the
foundation. The rhetorical and dialectical teaching as then given (he
tells us) was mere unscientific routine, prescribing specimens of art
to be committed to memory: respecting syllogism (or the conditions of
legitimate deductive inference) absolutely nothing had been said.[36]
Under these circumstances, his theory of names, notions, and
propositions as employed for purposes of exposition and
ratiocination, is a remarkable example of original inventive power.
He had to work it out by patient and laborious research. No way was
open to him except the diligent comparison and analysis of
propositions. And though all students have now become familiar with
the various classes of terms and propositions, together with their
principal characteristics and relations, yet to frame and designate
such classes for the first time without any precedent to follow, to
determine for each the rules and conditions of logical
convertibility, to put together the constituents of the Syllogism,
with its graduation of Figures and difference of Modes, and with a
selection, justified by reasons given, between the valid and the
invalid modes--all this implies a high order of original
systematizing genius, and must have required the most laborious and
multiplied comparisons between propositions in detail.
[Footnote 36: Aristot. Sophist. Elench. p. 184, a. 1, b. 2: [Greek:
dio/per tachei=a me\n a)/technos d' ê)=n ê( didaskali/a toi=s
mantha/nousi par' au)tô=n; ou) ga\r te/chnên a)lla\ ta\ a)po\ tê=s
te/chnês dido/ntes paideu/ein u(pela/mbanon . . . . _peri\ de\ tou=
sullogi/zesthai pantelô=s ou)de\n ei)/chomen pro/teron a)/llo
le/gein, a)ll' ê)\ tribê=| zêtou=ntes polu\n chro/non e)ponou=men_.]]
The preceding abridgment of Aristotle's exposition of the Syllogism
applies only to propositions simply affirmative or simply negative.
But Aristotle himself, as already remarked, complicates the
exposition by putting the Modal propositions (Possible, Necessary)
upon the same line as the above-mentioned Simple propositions. I have
noticed, in dealing with the treatise De Interpretatione, the
confusion that has arisen from thus elevating the Modals into a line
of classification co-ordinate with propositions simply Assertory. In
the Analytica, this confusion is still more sensibly felt, from the
introduction of syllogisms in which one of the premisses is
necessary, while the other is only possible. We may remark, however,
that, in the Analytica, Aristotle is stricter in defining the
Possible than he has been in the De Interpretatione; for he now
disjoins the Possible altogether from the Necessary, making it
equivalent to the Problematical (not merely _may be_, but _may be or
may not be_).[37] In the middle, too, of his diffuse exposition of
the Modals, he inserts one important remark, respecting universal
propositions generally, which belongs quite as much to the preceding
exposition about propositions simply assertory. He observes that
universal propositions have nothing to do with time, present, past,
or future; but are to be understood in a sense absolute and
unqualified.[38]
[Footnote 37: Analyt. Prior. I. viii. p. 29, a. 32; xiii. p. 32, a.
20-36: [Greek: to\ ga\r a)nagkai=on o(mônu/môs e)nde/chesthai
le/gomen]. In xiv. p. 33, b. 22, he excludes this equivocal meaning
of [Greek: to\ e)ndecho/menon--dei= de\ to\ e)nde/chestha lamba/nein
mê\ e)n toi=s a)nagkai/ois, a)lla\ kata\ to\n ei)rême/non